That's completely absurd, at least here in the U.S. If a psychiatrist involuntarily admitted someone just because the patient believed in a conspiracy theory they should be rightfully sued by the patient and would certainly win the case. That would be gross malpractice.

Moreover, there is no incentive for psychiatrists to be admitting people inappropriately. Psychiatrists are physicians and want to feel like they're actually doing something useful like everyone else. I have no interest in admitting a patient that doesn't have a treatable illness. There are plenty of patients with real illnesses to treat.